So, it turns out that I was easily able to access my father's (Bronx) and grandfather's (Manhattan) birth certificates. I just needed to supply original copies of their death certificates. For my dad's birth record (from Bronx County) I think I had to send some government issued pieces of mail to ...

Toasty:

My father is deceased and we never went to probate because he had very little assets. I'm assuming I can't file the small estate affidavit since he didn't reside in NY. Is that correct?

Man, NY makes things soooo unnecessarily difficult.